I've had a couple of non starting (not turning over) issues on my 156 v6 over the years...
First time, driving up the A2 then suddenly the engine died. AA guy checked all the usual stuff but was suspecting that the ECU had died!
To cut a long story short (full story on one of my posts) it turned out being the key code / immobiliser module (small black box with a green sticker, under the dash next to the steering column) that had suddenly died!
A brown fuse (7.5 amp iirc) tucked up above the main bank of fuses to the right of the steering column was also blown.
The AA guy said that there are fuses behind the glovebox, but he never got as far as checking them.
On the second occasion, it was a corroded pin on one of the relays in front of the battery.
I see that you've already checked the relays, but with the age of these cars now, it's also worth checking the connections on the underside of the relay box too.
"Looking through the knothole in Granny's wooden leg"